Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page

Considerations on rescattering effects for threshold photo- and electro-production of π0\pi^0 on deuteron

We show that for the S-state $\pi^0$-production in processes $\gamma+d\to d+\pi^0$ and $e^-+d\to e^-+d+\pi^0$ the rescattering effects due to the transition: $\gamma+d\to p+p+\pi^-$ (or $n+n+\pi^+)\to d+\pi^0$ are cancelled out due to the Pauli principle. The large values for these effects predicted in the past may result from the fact that the spin structure of the corresponding matrix element and the necessary antisymmetrization induced by the presence of identical protons (or neutrons) in the intermediate state was not taken into account accurately. One of the important consequences of these considerations is that $\pi^0$ photo- and electro-production on deuteron near threshold can bring direct information about elementary neutron amplitudes.Comment: Add a new sectio

Meissner effect, Spin Meissner effect and charge expulsion in superconductors

The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expand their orbits and thereby lower their quantum kinetic energy in the transition to superconductivity. Associated with this process, the metal expels negative charge from the interior to the surface and an electric field is generated in the interior. The resulting charge current can be understood as arising from the magnetic Lorentz force on radially outgoing electrons, and the resulting spin current can be understood as arising from a spin Hall effect originating in the Rashba-like coupling of the electron magnetic moment to the internal electric field. The associated electrodynamics is qualitatively different from London electrodynamics, yet can be described by a small modification of the conventional London equations. The stability of the superconducting state and its macroscopic phase coherence hinge on the fact that the orbital angular momentum of the carriers of the spin current is found to be exactly $\hbar/2$, indicating a topological origin. The simplicity and universality of our theory argue for its validity, and the occurrence of superconductivity in many classes of materials can be understood within our theory.Comment: Submitted to SLAFES XX Proceeding

Global well-posedness for the KP-I equation on the background of a non localized solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in $x$ and $y$ periodic or conversely)

Structural and optical studies of FeSb2 under high pressure

Nanostructured orthorhombic FeSb2 and an amorphous phase were formed by mechanical alloying starting from a mixture of high purity elemental Fe and Sb powders. The effects of high pressures on structural and optical properties were studied using X-ray diffraction (XRD) and Raman spectroscopy (RS). XRD patterns showed the presence of the orthorhombic FeSb2 phase up to the maximum pressure applied (28.2 GPa). The XRD patterns showed also an increase in the amount of the amorphous phase with increasing pressure up to 23.3 GPa. At 14.3 GPa, together with the former phases, a new phase was observed and indexed to a tetragonal FeSb2 phase, but its volume fraction is small at least up to 23.3 GPa. For the orthorhombic FeSb2 phase, the pressure dependence of the volume fitted to a Birch-Murnaghan equation of state gave a bulk modulus = 74.2 +- 3.0 GPa and its pressure derivative = 7.5 +- 0.6. RS measurements were performed from atmospheric pressure up to 45.2 GPa. For the orthorhombic FeSb2 phase, the Raman active mode was observed up to the maximum pressure applied, while the mode disappeared at 16.6 GPa. For pressures higher than 21 GPa, the Raman active mode of a tetragonal FeSb2 phase was observed, confirming ab initio calculations reported in the literature.Comment: 31 pages, 11 figures and 2 tables. Already submitted for publicatio

Laboratory Development

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Recent progress on the chiral unitary approach to meson meson and meson baryon interactions

We report on recent progress on the chiral unitary approach, analogous to the effective range expansion in Quantum Mechanics, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented. Results for the extension of these ideas to the meson baryon sector are discussed, together with applications to kaons in a nuclear medium and $K^-$ atoms.Comment: Contribution to the KEK Tanashi Symposium on Physics of Hadrons and Nuclei, Tokyo, December 1998, 10 pages, 3 postscript figures. To be published as a special issue of Nuclear Physics

Multiple Andreev Reflection and Giant Excess Noise in Diffusive Superconductor/Normal-Metal/Superconductor Junctions

We have studied superconductor/normal metal/superconductor (SNS) junctions consisting of short Au or Cu wires between Nb or Al banks. The Nb based junctions display inherent electron heating effects induced by the high thermal resistance of the NS boundaries. The Al based junctions show in addition subharmonic gap structures in the differential conductance dI/dV and a pronounced peak in the excess noise at very low voltages V. We suggest that the noise peak is caused by fluctuations of the supercurrent at the onset of Josephson coupling between the superconducting banks. At intermediate temperatures where the supercurrent is suppressed a noise contribution ~1/V remains, which may be interpreted as shot noise originating from large multiple charges.Comment: 7 pages, 7 figures, extended versio

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macro

Photoproduction of the Lambda(1405) on the proton and nuclei

We study the gamma p ---> K^+ Lambda(1405) reaction at energies close to threshold using a chiral unitary model where the resonance is generated dynamically from K^-p interaction with other channels constructed from the octets of baryons and mesons. Predictions are made for cross sections into several channels and it is shown that the detection of the K^+ is sufficient to determine the shape and strength of the Lambda(1405) resonance. The determination of the resonance properties in nuclei requires instead the detection of the resonance decay channels. Pauli blocking effects on the resonance, which have been shown to be very important for the resonance at rest in the nucleus, are irrelevant here where the resonance is produced with a large momentum. The nuclear modifications here would thus offer information on the resonance and K^- nucleus dynamics complementary to the one offered so far by K^- atoms.Comment: 9 pages, 4 postscripts figure